Finite Group Databasebeta

← #27186506

Subgroups — #27186506

Order 12928.

238 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20266195C211yesmaximal, characteristic, complemented
2#20266113C211yesmaximal, characteristic, complemented
3#20266030C212yesmaximal, complemented
4#20266029C212yesmaximal
5#20265712C211yesmaximal, characteristic
6C2×C4×#87938—21no—
7#15692322—21no—
8#15692312C2212yes—
9C4×#11717581—21no—
10(C2×#87938)⋊C4—21no—
11(C2×#87938)⋊C4C2212yes—
12#15692250—21no—
13#15692243C411yescharacteristic, complemented
14#15692240—21no—
15#15692235C2211yescharacteristic
16#15692230C2211yescharacteristic
17#15692220C411yescharacteristic, complemented
18#15692217—21no—
19#15692217C411yescharacteristic, complemented
20#15692213—21no—
21C42×D101C2211yescharacteristic
22#125×C101C411yescharacteristic, complemented
23C22×#87938—22no—
24C2×#11717581—22no—
25C4×#87938—24no—
26C2×Dic202C2×C411yescharacteristic
27C2×D404—21no—
28C2×D404C2×C411yescharacteristic
29C2×C4×D101—21no—
30C2×C4×D101D411yescharacteristic
31C2×C4×D101D411yescharacteristic
32C2×C4×D101C2311yescharacteristic
33C4⋊Dic101—21no—
34#13108053—21no—
35#13108051—21no—
36#13108051—21no—
37#13108051—21no—
38#13108051—21no—
39#13108051—21no—
40C4×Dic101—21no—
41C4×Dic101C2×C411yescharacteristic
42C4×Dic101D411yescharacteristic
43C4×Dic101D411yescharacteristic
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101C2×C411yescharacteristic
47C4⋊C4×C101C2×C411yescharacteristic
48C42×C101C2×C411yescharacteristic
49C22×D101—21no—
50C22×D101C2×D411yescharacteristic
51C2×#87938—24no—
52C2×#87938—42no—
53C2×#87938—42no—
54C2×C4×C101—21no—
55C2×C4×C101—21no—
56C2×C4×C101C22⋊C411yescharacteristic
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22×C411yescharacteristic
59C2×Dic101—21no—
60C2×Dic101C22⋊C411yescharacteristic
61C2×Dic101C22⋊C411yescharacteristic
62C2×Dic101C2×D411yescharacteristic
63D404—41no—
64D404—42no—
65C4×D101—22no—
66C4×D101—22no—
67C4×D101—41no—
68C4×D101—42no—
69Dic202—41no—
70#11717581—42no—
71C22×C101C2×C22⋊C411yescharacteristic
72C2×D101—21no—
73C2×D101—21no—
74C2×D101—41no—
75C2×D101—41no—
76C2×D101—41no—
77C2×D101#13512yes—
78#87938—44no—
79C4×C101—21no—
80C4×C101—21no—
81C4×C101—21no—
82C4×C101—41no—
83C4×C101—41no—
84Dic101—21no—
85Dic101—21no—
86Dic101—41no—
87Dic101#10412yes—
88C2×C101#41011yescharacteristic
89C2×C101#41611yescharacteristic
90C2×C101C2×#10411yescharacteristic
91D101—22no—
92D101—81no—
93#1500—1011nomaximal, Sylow
94C101#150011yescharacteristic, complemented, Sylow
95#529—1011no—
96#431—1011no—
97#376—1011no—
98#328—1012no—
99#327—1012no—
100#126—2021no—
101#125#8793811yescharacteristic, complemented
102#124—1011no—
103#123—2021no—
104C22⋊Q8—1011no—
105#121—1011no—
106C4×Q8—1011no—
107C4×D4—1011no—
108C4×D4—2021no—
109#117—2021no—
110C2×C42—1011no—
111C2×C42—2021no—
112C4⋊C8—2021no—
113C22⋊C8—1012no—
114C4×C8—2021no—
115#95—1012no—
116#95—2021no—
117C2×Q8—1011no—
118C2×D4—1011no—
119C2×D4—2021no—
120C22×C4—1011no—
121C22×C4—1011no—
122C22×C4—1011no—
123C22×C4—2021no—
124C22×C4—2022no—
125C2×C8—2022no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4C2×#8793811yescharacteristic
131C4⋊C4C2×#8793811yescharacteristic
132C22⋊C4—2021no—
133C22⋊C4—2021no—
134C22⋊C4—2021no—
135C22⋊C4—2021no—
136C22⋊C4—2021no—
137C42—1011no—
138C42—1011no—
139C42—1011no—
140C42—2021no—
141C42—2024no—
142C42C2×#8793811yescharacteristic
143C23—1011no—
144C23—2021no—
145Q8—4041no—
146D4—4041no—
147D4—4042no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—1011no—
151C2×C4—1011no—
152C2×C4—1011no—
153C2×C4—4041no—
154C2×C4—4042no—
155C2×C4—4042no—
156C2×C4—4042no—
157C2×C4—2022no—
158C2×C4—2022no—
159C2×C4—2024no—
160C2×C4—2021no—
161C2×C4C22⋊#8793811yescharacteristic
162C2×C4C22⋊#8793811yescharacteristic
163C2×C4C22×#8793811yescharacteristic
164C8—4042no—
165C22—1012no—
166C22—4041no—
167C22—4041no—
168C22—4041no—
169C22—2021no—
170C22—2021no—
171C22C2×C22⋊#8793811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—1012no—
178C4—4044no—
179C4—4041no—
180C4—2021no—
181C4—2021no—
182C2—8081no—
183C2—2022no—
184C2#2026615811yescharacteristic
185C2#2026616711yescharacteristic
186C2D101⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#125×C101C4
socleC22×C101C2×C22⋊C4
prime radical#15692230C22
cosocleC2×C4×D101C23
hypercenter#125#87938
hypocenterC101#1500
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20266195C2semidirect
2. #20266113C2semidirect
3. #20266030C2semidirect
13. #15692243C4semidirect
17. #15692220C4semidirect
19. #15692217C4semidirect
22. #125×C101C4semidirect
94. C101#1500semidirect
101. #125#87938semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202661952
#202661132
#202660302
#202660292
#202657122
#1500101